I've haven't really had a commercial salad dressing in a long time because they are full of things you shouldn't eat (even good ones like Renee's, unfortunately), so I always make my own from scratch. Before doing the BTD, I would mix some kind of oil with some kind of vinegar and a touch of salt and pepper and call it a day. If you can still have vinegar, I recommend almond oil and red wine vinegar - it's delicious.
Vinegars of all kinds are forbidden to A's and AB's, so I made citronettes. Citronettes are dressings made with a citrus of some kind plus oil, with the citrus replacing the vinegar in a vinaigrette. The world of citrus for A's and AB's extends to lemons, limes and grapefruit. This is the salad dressing I use every day. You can make as much or as little as you like. It keeps in the fridge for about a week.
Juice of 1/2 a lemon
About the same amount of extra virgin olive oil (slightly less for those who prefer a sharper-tasting dressing)
small pinch of sea salt
1/8 tsp dry mustard powder (I use Keen's)
small squirt of honey, about 1/4-1/2 tsp
Whisk all ingredients together until well-blended. Enjoy with salad of your choice.